Question
Three friends decide that they each want to be able to buy a new boat in five years.
Vanore puts $1,000 in a savings account with a simple interest rate of 4.5%.
Keir invests $1,200 in a standard savers account with a simple interest rate of 4%.
Omar invests $950 in a junior achievers account with a 6% annual compound interest rate.
Who will have the most money to spend on a new boat at the end of the five years? Use the formula I = P r t for simple interest and A = P (1 + r) Superscript t for compound interest. Round to the nearest dollar.
Keir will have $1,440, the most money for the boat.
Vanore will have the most money, $1,271, for the boat.
Omar will have the most money, $1,271, for the boat.
Vanore will have $1,440, the most money for the boat
Vanore puts $1,000 in a savings account with a simple interest rate of 4.5%.
Keir invests $1,200 in a standard savers account with a simple interest rate of 4%.
Omar invests $950 in a junior achievers account with a 6% annual compound interest rate.
Who will have the most money to spend on a new boat at the end of the five years? Use the formula I = P r t for simple interest and A = P (1 + r) Superscript t for compound interest. Round to the nearest dollar.
Keir will have $1,440, the most money for the boat.
Vanore will have the most money, $1,271, for the boat.
Omar will have the most money, $1,271, for the boat.
Vanore will have $1,440, the most money for the boat
Answers
GPT-4o mini
To determine who will have the most money at the end of five years, we need to calculate the total amount for each friend using the given formulas.
### Vanore's Investment
- **Principal (P)** = $1,000
- **Rate (r)** = 4.5% = 0.045
- **Time (t)** = 5 years
**Simple Interest Formula:**
\[ I = P \cdot r \cdot t \]
\[ I = 1000 \cdot 0.045 \cdot 5 \]
\[ I = 1000 \cdot 0.225 = 225 \]
**Total Amount (A):**
\[ A = P + I \]
\[ A = 1000 + 225 = 1225 \]
### Keir's Investment
- **Principal (P)** = $1,200
- **Rate (r)** = 4% = 0.04
- **Time (t)** = 5 years
**Simple Interest Formula:**
\[ I = P \cdot r \cdot t \]
\[ I = 1200 \cdot 0.04 \cdot 5 \]
\[ I = 1200 \cdot 0.2 = 240 \]
**Total Amount (A):**
\[ A = P + I \]
\[ A = 1200 + 240 = 1440 \]
### Omar's Investment
- **Principal (P)** = $950
- **Rate (r)** = 6% = 0.06
- **Time (t)** = 5 years
**Compound Interest Formula:**
\[ A = P \cdot (1 + r)^t \]
\[ A = 950 \cdot (1 + 0.06)^5 \]
\[ A = 950 \cdot (1.06)^5 \]
Calculating \( (1.06)^5 \):
\[ (1.06)^5 \approx 1.338225 \]
Thus,
\[ A \approx 950 \cdot 1.338225 \approx 1271.81475 \]
**Total Amount (rounded):**
\[ A \approx 1272 \]
### Summary of Total Amounts:
- Vanore: $1,225
- Keir: $1,440
- Omar: $1,272
### Conclusion:
Keir will have the most money for the boat, with a total of **$1,440**.
So the correct choice is:
**Keir will have $1,440, the most money for the boat.**
### Vanore's Investment
- **Principal (P)** = $1,000
- **Rate (r)** = 4.5% = 0.045
- **Time (t)** = 5 years
**Simple Interest Formula:**
\[ I = P \cdot r \cdot t \]
\[ I = 1000 \cdot 0.045 \cdot 5 \]
\[ I = 1000 \cdot 0.225 = 225 \]
**Total Amount (A):**
\[ A = P + I \]
\[ A = 1000 + 225 = 1225 \]
### Keir's Investment
- **Principal (P)** = $1,200
- **Rate (r)** = 4% = 0.04
- **Time (t)** = 5 years
**Simple Interest Formula:**
\[ I = P \cdot r \cdot t \]
\[ I = 1200 \cdot 0.04 \cdot 5 \]
\[ I = 1200 \cdot 0.2 = 240 \]
**Total Amount (A):**
\[ A = P + I \]
\[ A = 1200 + 240 = 1440 \]
### Omar's Investment
- **Principal (P)** = $950
- **Rate (r)** = 6% = 0.06
- **Time (t)** = 5 years
**Compound Interest Formula:**
\[ A = P \cdot (1 + r)^t \]
\[ A = 950 \cdot (1 + 0.06)^5 \]
\[ A = 950 \cdot (1.06)^5 \]
Calculating \( (1.06)^5 \):
\[ (1.06)^5 \approx 1.338225 \]
Thus,
\[ A \approx 950 \cdot 1.338225 \approx 1271.81475 \]
**Total Amount (rounded):**
\[ A \approx 1272 \]
### Summary of Total Amounts:
- Vanore: $1,225
- Keir: $1,440
- Omar: $1,272
### Conclusion:
Keir will have the most money for the boat, with a total of **$1,440**.
So the correct choice is:
**Keir will have $1,440, the most money for the boat.**